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Convergence rate of Tsallis entropic regularized optimal transport
Takeshi Suguro, Toshiaki Yachimura · 2023-04-13 · via stat.ML updates on arXiv.org

In this paper, we study the Tsallis entropic regularized optimal transport in the continuous setting and establish fundamental results such as the $Γ$-convergence of the Tsallis regularized optimal transport to the Monge--Kantorovich problem as the regularization parameter tends to zero. In addition, using the quantization and shadow arguments developed by Eckstein--Nutz, we derive the convergence rate of the Tsallis entropic regularization and provide explicit constants. Furthermore, we compare these results with the well-known case of the Kullback--Leibler (KL) divergence regularization and show that the KL regularization achieves the fastest convergence rate in the Tsallis framework.

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